How to create a (nxn) matrix with alternating sign

How do i create a (n x n) matrix whose elements are either +3 or –3 such that the sign of each element is different from its adjacent elements, both from those above and below it and from those on either side of it (see Y below).

Answer 1

[Paulo Silva]

Just for fun, here's how it can be done with loops

n=3; %value chosen
r=3; %number of rows
c=3; %number of columns
m=zeros(r,c); %pre-allocate output
for cc=1:c %do it for all columns
    for rr=1:r %do it for all rows
        m(rr,cc)=n*(-1)^(rr+cc); %put the value in the place
    end
end
m %the output

[Matt Fig]

+1 The only single solution offered as of now which works for both even and odd n.

[Teja Muppirala]

Ouch. Indeed. I take my solution back.

Answer 2

[Matt Fig]

Here is another which works for even or odd n.

M = toeplitz((-1).^(1:n));

And even faster (very much so for large n!)...

    M = (-1).^(1:n);
    M = 3*M.'*M

Note that this can be generalized, like Paulo's solution, to m-by-n.

M = 3*((-1).^(1:m).')*((-1).^(1:n))

EDIT .

.

What is surprising to me is that this is even faster than the above for large m,n:

M = zeros(m,n);
M(:,1) = 3*((-1).^(0:m-1).');

for ii = 2:n
    M(:,ii) = (-1)^(ii+1)*M(:,1);
end

[Walter Roberson]

You won the fastest-to-the-button this time!

[Jan]

"1-2*rem(x, 2)" is faster than "(-1)^x".

Answer 3

[bym]

b =

    -3     3
     3    -3
   b=repmat(b,3,3)
b =

    -3     3    -3     3    -3     3
     3    -3     3    -3     3    -3
    -3     3    -3     3    -3     3
     3    -3     3    -3     3    -3
    -3     3    -3     3    -3     3
     3    -3     3    -3     3    -3

[Patrick]

I want to have the user specify n and do this with a for loop i think.

[Oleg Komarov]

Why a for loop?

Answer 4

[Walter Roberson]

For odd n

m = 3 * ones(n);
m(1:end) = m(1:end) .* (-1).^(1:numel(m));

Or, for even n,

m = kron(3 * ones(n/2), [-1 1;1 -1]);

Answer 5

[Sean de Wolski]

%And a BSXFUN solution

n = 3;
r = 4;
c = 5;
m = bsxfun(@(x,y)n*(-1).^(x+y),(1:r).',1:c)